I ran nmap -p- -PN on my home IP address. I'm using a VPN so presumably the scan is what the outside world would see if they ran nmap. The scan returned

PORT STATE SERVICE
10605/tcp open unknown
38864/tcp open unknown

My devices are connected to the Internet through a Linksys E1000 router. What are these ports for? Why are they open on the router? Can I close them? And is there a way to see what services (I have two machines, one running Win7 and the other running Ubuntu -- oh and also e-readers and cell phones) might be using them?

Doesn't look like they are known for anything specific: en.wikipedia.org/wiki/List_of_TCP_and_UDP_port_numbers. You can use netstat -bf on the win7 machine to see if they are in use and where they are connected to. I'm sure there is a similar netstat command for ubuntu you can use.
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MaQleodNov 14 '11 at 3:00

Do you have UPNP enabled in the router configuration? They could have been opened by an internal service if so.
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PaulNov 14 '11 at 4:52